Questions tagged [math]

For questions about mathematics related to artificial intelligence.

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27
votes
4answers
4k views

Can neural networks be used to prove conjectures?

Imagine I have a list (in a computer-readable form) of all problems (or statements) and proofs that math relies on. Could I train a neural network in such a way that, for example, I enter a problem ...
20
votes
1answer
6k views

What is the Bellman operator in reinforcement learning?

In mathematics, the word operator can refer to several distinct but related concepts. An operator can be defined as a function between two vector spaces, it can be defined as a function where the ...
3
votes
4answers
507 views

What is the fundamental difference between an ML model and a function?

A model can be roughly defined as any design that is able to solve an ML task. Examples of models are the neural network, decision tree, Markov network, etc. A function can be defined as a set of ...
17
votes
3answers
1k views

What are the mathematical prerequisites for an AI researcher?

What are the mathematical prerequisites for understanding the core part of various algorithms involved in artificial intelligence and developing one's own algorithms? Please, refer some specific books....
29
votes
5answers
20k views

Is it possible to train the neural network to solve math equations?

I'm aware that neural networks are probably not designed to do that, however asking hypothetically, is it possible to train the deep neural network (or similar) to solve math equations? So given the ...
4
votes
1answer
2k views

Why does the “reward to go” trick in policy gradient methods work?

In the policy gradient method, there's a trick to reduce the variance of policy gradient. We use causality, and remove part of the sum over rewards so that only actions happened after the reward are ...
4
votes
2answers
164 views

Mathematical foundations of the ability to learn

I am an undergraduate student in applied mathematics with an interest in artificial intelligence. I am currently exploring topics where I could do research. Coming from a mathematical background I am ...
4
votes
1answer
227 views

Which functions can be activation functions?

What are the required characteristics of an activation function (in a neural network)? Which functions can be activation functions? For example, which of the functions below can be used as an ...
18
votes
6answers
16k views

How does one start learning artificial intelligence? [duplicate]

I am a software engineering student and I am complete beginner to AI. I have read a lot of articles on how to start learning AI, but each article suggests a different way. I was wondering if some of ...
13
votes
3answers
2k views

What sort of mathematical problems are there in AI that people are working on?

I recently got a 18-month postdoc position in a math department. It's a position with relative light teaching duty and a lot of freedom about what type of research that I want to do. Previously I was ...
9
votes
3answers
4k views

What are the mathematical prerequisites to be able to study artificial general intelligence?

What are the mathematical prerequisites to be able to study artificial general intelligence (AGI) or strong AI?
11
votes
2answers
1k views

How do we prove the n-step return error reduction property?

In section 7.1 (about the n-step bootstrapping) of the book Reinforcement Learning: An Introduction (2nd edition), by Andrew Barto and Richard S. Sutton, the authors write about what they call the "n-...
2
votes
4answers
375 views

Can we define the AI singularity mathematically?

The "AI Singularity" or "Technological Singularity" is a vague term that roughly seems to refer to the idea of: Humans can design algorithms Humans can improve algorithms Eventually algorithms we ...
8
votes
3answers
940 views

How can I start learning mathematics for machine learning?

I am an Android programmer. Now, I would like to learn machine learning. I know it requires a mathematical background, like statistics, probability, calculus and linear algebra. However, I am a bit ...
10
votes
5answers
5k views

Why do activation functions need to be differentiable in the context of neural networks?

Why should an activation function of a neural network be differentiable? Is it strictly necessary or is it just advantageous?
7
votes
2answers
92 views

Interpretation of inverse matrix in mean calculation in Gaussian Process

The formula for mean prediction using Gaussian Process is $k(x_*, x)k(x, x)^{-1}y$, where $k$ is the covariance function. See e.g. equation 2.23 (in chapter 2) from Gaussian Processes for Machine ...
6
votes
1answer
163 views

Can deep learning be used to help mathematical research?

I am currently learning about deep learning and artificial intelligence and exploring his possibilities, and, as a mathematician at heart, I am inquisitive about how it can be used to solve problems ...
3
votes
1answer
1k views

What does the Markov assumption say about the history of state sequences?

Does the Markov assumption say that the conditional probability of the next state only depends on the current state or does it say that the conditional probability depends on a fixed finite number of ...
6
votes
2answers
980 views

How is local minima possible in gradient descent?

Gradient descent works on the equation of mean squared error, which is an equation of a parabola $y=x^2$. We often say that weight adjustment in a neural network by gradient descent algorithm can hit ...
4
votes
1answer
118 views

Why is my derivation of the back-propagation equations inconsistent with Andrew Ng's slides from Coursera?

I am using the cross-entropy cost function to calculate its derivatives using different variables $Z, W$ and $b$ at different instances. Please refer image below for calculation. As per my knowledge, ...
2
votes
1answer
106 views

How is the log-derivative trick of a trajectory derived?

I am looking at this formula which breaks down the gradient of $P(\tau |\theta)$ the first part is clear as is the derivative of $\log(x)$, but I do not see how the first formula is rearranged into ...
1
vote
1answer
293 views

Understanding the derivation of the first-order model-agnostic meta-learning

According to the authors of this paper, to improve the performance, they decided to drop backward pass and using a first-order approximation I found a blog which discussed how to derive the math ...
0
votes
1answer
54 views

Do the rows of the design matrix refer to the observations or predictors?

I attempt to understand the formulation of dictionary learning for this paper: Depression Detection via Harvesting Social Media: A Multimodal Dictionary Learning Solution Multimodal Task-Driven ...
-4
votes
2answers
668 views

What are the approaches to predict sequence of π numbers? [closed]

Given list of fixed numbers from a mathematical constant such as Pi, is it is possible to train AI to attempt to predict the next numbers? Which AI or neural network would be more suitable for this ...